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Fundamentals & applications of plasmonics
Svetlana V. Boriskina
Lecture 2/2
S.V. Boriskina, 2012
Overview: lecture 2• Recap of Lecture 1• Refractive index sensing• SP-induced nanoscale optical forces
– Optical trapping & manipulation of nano-objects• Fluorescence & Raman spectroscopy• Plasmonics for photovoltaics• Hydrodynamic design of plasmonic components• Magnetic effects• Thermal effects:
– Plasmonic heating– Near-field heat transfer via SPP waves
• Plasmonic photosensitization of materials• Further reading & software packages• Omitted topics
S.V. Boriskina, 2012
Drude-Lorentz-Sommerfeld theory
Image credit: Wikipedia
Collision frequency
electron velocity
mean free path
lv 1
)(1)(
2
2
ipDrude
permittivity function:
ep mne 022 Plasma
frequency
S.V. Boriskina, 2012
Recap of Lecture 1: Propagating waves
Frequency (Quasi)particle Dispersion equation
Plane wave
transversephoton
Bulk plasmonlongitu-
dinal
plasmonmetals:
semicond.:
Surface plasmon
TM: E=(Ex,0,Ez)
polariton =photon + plasmon
21
dm
dmx ck
dx ck
21221px c
k e
p m
ne
0
2
d
p
1
eV10p
eV5.0p
ω
kx(ω)
p
dp 1
p
dp 1
p
High DOS, high localization
S.V. Boriskina, 2012
Recap of Lecture 1: Localized plasmonsScattering response Schematic dipoles Near-field
patterns
Plasmonic atom
Plasmonic molecules
Plasmonic antenna
array
High D
OS, high localization
Movie: http://juluribk.com
E
+++
- - -
Lowest-energy modes
λ
quadrupole
dipole
dimer heptamer
S.V. Boriskina, 2012
Plasmons interactions with matter• Optical
– Extreme light focusing/localization (sub-resolution imaging, photovoltaics)
– Strong sensitivity to environmental changes (sensing) – Amplification of weak molecular signals (fluorescence, Raman
scattering, absorption, circular dichroism)
• Electronic– Enhancement of catalytic reactions– Plasmonic photosensitization of materials
• Mechanical – Mechanical manipulation of nanoobjects
• Thermal– Selective heating of nanoscale areas– Enhanced near-field heat transfer
S.V. Boriskina, 2012
SP-enhanced sensing
n
FoM
Resonance linewidth
Sensitivity
Sensor figure of merit (FoM):
http://www.bio-sensors.net
SPP sensors
McFarland, A.D. & R.P. Van Duyne, Nano Lett. 2003. 3(8): p. 1057-1062.
LSP sensors
Requirements:•High sensitivity•High spectral resolution•Compact design
S.V. Boriskina, 2012
FOM enhancement & miniaturization• Fano resonances in plasmonic molecules
Mirin, N.A., K. Bao, & P. Nordlander, J. Phys. Chem. A, 2009. 113(16): p. 4028-4034.
S.V. Boriskina, 2012
Towards single-molecule sensitivityHybrid modes in optoplasmonic molecules:
Santiago-Cordoba, M.A. et al, Appl. Phys. Lett., 2011. 99: p. 073701. Also: Boriskina, S.V. & B.M. Reinhard, Opt. Express, 2011. 19(22): 22305-22315; Ahn, W. et al, ACS Nano, 2012. 6(1): 951-960.
S.V. Boriskina, 2012
Rayleigh ground
excited
virtual (induced dipole)
hν0
Raman spectroscopy Rayleigh scattering
Raman scattering
hν0 hν0
h(ν0 ± νm)hν0
νm - molecular fingerprint
Stokes Raman
vibrat.hνm
Raman – Nobel Prize in 1930
)cos( 00 tE
Dipole moment induced by light:
polarizability tensor
qqq 0)( vibrational coordinate
)cos(0 tqq m
t
tEq
qtE
m
m
)(cos
)(cos)cos(
0
00000
Rayleigh Raman (Stokes & anti-Stokes)
4
6
R ~ d
Iparticle size
R3
Ram 10~ II
a very weak effect!
S.V. Boriskina, 2012
Surface enhanced Raman spectroscopy (SERS)
Fleischman M,et al Chem. Phys. Lett. 1974; 26: 123.Jeanmaire DL, Duyne RPV. J. Electroanal. Chem. 1977; 84: 1.
0Ram ~ EggE R
Review: Moskovits, M., J. Raman Spectr., 2005. 36(6-7): p. 485-496 +references therein
E-field enhancement @ ν0 E-field enhancement @ (ν0 –νm)
High field localization enables SERS fingerprinting of single molecules
Nie, S. & S.R. Emory, Science, 1997. 275(5303): 1102-1106.
R6G molecules on Ag nanoparticles
@ the molecule position!
S.V. Boriskina, 2012
Single molecule delivery to the SP hot spot
De Angelis, F., et al. Nat Photon. 5(11): p. 682-687.
• super-hydrophobic delivery:
S.V. Boriskina, 2012
Single molecule delivery to the SP hot spot
• Optical trapping:
Review: Juan, M.L. et al, Nat Photon, 2011. 5(6): p. 349-356
)"'(0
0 GGc
nIFU D kF
Gradient force
Dissipative force
Intensity enhancementThe probability to find
a molecule @ r :
Optical potential
L. Novotny, et al, Phys. Rev. Lett. 79 (4), 645 (1997); H. Xu and M. Käll, Phys. Rev. Lett. 89 (24), 246802 (2002).
10)( TkU Br
Stable trapping:
S.V. Boriskina, 2012
SP-enhanced fluorescence Fluorescence
Fluorescence rate of a dipole with moment μ:
)( nrrrexcf hνexc hνf
non-radiative rate (resistive
heating)radiative rateexcitation rate
2),( excmexc rEμ
Excitation rate:
),(3
2)(
2
0fmnrr
rμ
Fermi’s golden rule:
Local density of states
Spacer is needed to avoid quenching
The emission intensity affected by boththe excitation & emission modification Anger, P., P. Bharadwaj & L. Novotny,
Phys. Rev. Lett., 2006. 96(11): p. 113002
S.V. Boriskina, 2012
SP-enhanced fluorescence
Russell, K.J., et al., Nat Photon, 2012. advance online publication.
),(3
2)(
2
0fmnrr
rμ
Emission spectrum shaping by the high-LDOS nanoparticle resonances
Kinkhabwala, A., et al. Nature Photon., 2009. 3(11): p. 654-657.
Single-molecule fluorescence
See also a review: Ming, T., et al., J. Phys. Chem. Lett. 3(2): p. 191-202 (2012).
S.V. Boriskina, 2012
optical absorption
H. Atwater & A. Polman, Nature Mater. 2010
Plasmonic solar cells
charge carrier diffusion
c-Si: 250 - 700 μma-Si: 0.1 – 0.3 μm
Electronic/photonic lengths mismatch
S.V. Boriskina, 2012
Efficient nanoscale light trappingincrease of the local density of optical states in a certain frequency range
Callahan et al, Nano Lett. 2012
Atwater & Polman, Nature Mater. 2010
scattering field enhancement waveguiding
S.V. Boriskina, 2012
extinction cross-section
How can a particle absorb more than the light incident upon it? C.F. Bohren, Am J. Phys. 1983, 51(4), p.326
HES Re21 Poynting vectordetermines electromagnetic power flow
powerflow saddle pointW. Ahn, S.V. Boriskina, et al, Nano Lett. 12, 219-227 (2012)
S.V. Boriskina, 2012
Optical energy flows in the direction of the phase changephase saddle
flow saddle
phase vortex
flow vortex
Local topological features (sources, saddle points, vortices & sinks) define phase landscape that governs optical power flow vortex nanogear transmission
W. Ahn, et al, Nano Lett. 12, 219-227 (2012)
kv g group velocity
S.V. Boriskina, 2012
Reconfigurable vortex transmissions
S.V. Boriskina & B.M. Reinhard, Nanoscale, 4, 76-90, 2012
S.V. Boriskina, 2012
‘… the title is straight out of Enterprise's engineering room’
NextBigFuture.com SciTech forum
Reconfigurable vortex transmissions:vortex nanogates
Physical picture behind vortex nanogate
S.V. Boriskina, 2012
Hydrodynamic design of SP componentsElectromagnetics
?Maxwell’s equations:
t
t
ΕJH
HE
H
E
0
Gauss’ law
Gauss’ law for magnetism
Faraday’s law
Ampere’s law
+ boundary conditions
Continuity (mass conservation) equation
Momentum conservation equation
Navier-Stokes equations:
0)( v t
fT
vvv
p
t )(
fluid density flow velocity
Fluid dynamics
S.V. Boriskina, 2012
Hydrodynamic form of Maxwell’s equations
2|)(|)()( rUrr I
)(rv
‘Photon fluid’ density:
‘Photon fluid’ velocity:
))((exp)(),( tit rrUrE
Madelung transformation:
S.V. Boriskina & B.M. Reinhard, Nanoscale, 4, 76-90, 2012
convective term
)()()()( rrrvr
)()()()( rrrvrv QV
‘mass’ conservation:
momentum conservation:
)(12)( 20 rr kV
external potential created by the nanostructure
)()( 20 rr k
material loss or gain
• steady state flow• local convective acceleration possible• fluid flux (the momentum density):
)()()2(1 0 rvrS
S.V. Boriskina, 2012
Hydrodynamic form of Maxwell’s equations
)()()()( rrrvrv QV
Vortex generates a velocity field:
S.V. Boriskina & B.M. Reinhard, Nanoscale, 4, 76-90, 2012
S.V. Boriskina, 2012
Energy flows in plasmonic nanostructures
Surface plasmon polariton wave:
Stockman’s nanolens:
Li, K., M.I. Stockman, & D.J. Bergman, Phys. Rev. Lett., 2003. 91(22): p. 227402.
S.V. Boriskina & Reinhard, Nanoscale, 4, 76-90, 2012
S.V. Boriskina, 2012
Magnetic SP effects
t HE
Plasmonic nanostructures built from nonmagnetic materials can exhibit effective magnetic permeability
Image: http://www.ndt-ed.org/
coil magnet
rotating currents in the rings induce magnetic flux
effective permeability
Split-ring resonator:
Pendry, J.B. et al, IEEE Trans. Microw. Theory Tech., 47(11), p.2075, 1999
double-negative metamaterials
Shelby, R.A., et al Science, 2001. 292(5514): p. 77-79.
S.V. Boriskina, 2012
Magnetic SP effects in nanoparticle clusterst HE
Liu, N., et al., Nano Letters, 2011. 12(1): p. 364-369.
charge density:
induced magnetic moments:
Anti-ferromagnetic response:
dy
yz
x
dx
2r
Ag
E
k
dy
yz
x
yz
x
dx
2r
Ag
E
k
E
kElectric field intensity:
Magnetic field distribution:S.V. Boriskina, in Plasmonics in metal nanostructures: Theory & applications ( Shahbazyan & Stockman eds.) Springer, 2012
Magnetic dipole
Fan, J.A., et al. Science, 2010. 328(5982): p. 1135-1138.
S.V. Boriskina, 2012
Thermal SP effects
Electric field to heat:
),(),(~ tttT rErj dissipation of optical energy
temperature
nanopatterning
Atanasov, P.A., et al., Int. J. Nanopart. 2010. 3(3): p. 206-219.
cancer treatment
Chen, J., et al. Small, 2010. 6(7): p. 811-817.
Govorov A.O. & Richardson, Nano Today, 2007. 2(1) 30-38
S.V. Boriskina, 2012
Thermal SP effectsHeat to electric field:
V
dGi '),'(),',(),( 0 xxjxxrE fluctuating currents
~ DOS
Near-field heat transfer:
e.g., Narayanaswamy, A. & G. Chen, Appl. Phys. Lett. 2003. 82(20): p. 3544-3546; Fu, C.J. & W.C. Tan, J. Quant. Spectr. Radiat. Transf. 2009. 110(12): p. 1027-1036; Rousseau, E., et al. Nat Photon, 2009. 3(9): p. 514-517; Volokitin, A.I. & B.N.J. Persson. Rev. Mod. Phys., 2007. 79(4): p. 1291-1329
(cold, T2)
(hot, T1)+-+ -
+ -+-
High SPP-induced DOS results in the near-field coherence
d
S.V. Boriskina, 2012
Plasmonic photosensitization of semiconductors
• hot electrons can tunnel from metal nanoantennas into semiconductor• photon detection at energies below the semiconductor band gap
Knight, M.W., et al., Science. 332(6030): p. 702-704.
Theoretical prediction: Shalaev, V.M., et al., Phys. Rev. B, 1996. 53(17): p. 11388-11402.
S.V. Boriskina, 2012
Plasmonic enhancement of photocurrent
Mubeen, S., et al., Nano Letters. 11(12): p. 5548-5552.
Xu, G., et al (2012), Adv. Mater., 24: OP71–OP76
Echtermeyer, T.J., et al. 2012,
Nature Commun. 2: p. 458.
in silicon:
in graphene:
S.V. Boriskina, 2012
Books & review articles on plasmonics:
• Lal, S., S. Link, and N.J. Halas, Nano-optics from sensing to waveguiding. Nat Photon, 2007. 1(11): p. 641-648
• Halas, N.J., et al., Plasmons in strongly coupled metallic nanostructures. Chem. Rev., 2011. 111(6): p. 3913-3961
• Schuller, J.A., et al., Plasmonics for extreme light concentration and manipulation. Nature Mater., 2010. 9(3): p. 193-204
• Stockman, M.I., Nanoplasmonics: past, present, and glimpse into future. Opt. Express. 2011, 19(22): p. 22029-22106
• Maier, SA, Plasmonics: Fundamentals and Applications, Springer, NY, 2007• Novotny, L., and B. Hecht. Principles of Nano-Optics, Cambridge University
Press, 2006
This list is by no means complete …
S.V. Boriskina, 2012
Commercial & free software
• Lumerical FDTD Solutions http://www.lumerical.com/tcad-products/fdtd/• COMSOL Multiphysics® (FEM) http://www.comsol.com/products/multiphysics/• MEEP (FDTD)http://ab-initio.mit.edu/wiki/index.php/Meep• DDSCAT (discrete dipole approximation)http://www.astro.princeton.edu/~draine/DDSCAT.html• A collection of free software (including Mie theory methods)http://www.scattport.org/index.php/light-scattering-software
S.V. Boriskina, 2012
Topics I had to omit due to the lack of timePlasmonic cloaking:New Journal of Physics, Focus Issue on 'Cloaking and Transformation Optics', Guest Editors: Ulf Leonhardt and David R. Smith, Vol. 10, Nov 2008.
Non-local response:A.D. Boardman, Electromagnetic Surface Modes, Ch. Hydrodynamic Theory of Plasmon–polaritons on Plane Surfaces, John Wiley & Sons Ltd., 1982.
Resonant energy transfer & ‘dark’ plasmonic nanocircuits:Andrew, P. and W.L. Barnes, Energy Transfer Across a Metal Film Mediated by Surface Plasmon Polaritons. Science, 2004. 306(5698): p. 1002-1005Akimov, A.V., et al., Generation of single optical plasmons in metallic nanowires coupled to quantum dots. Nature, 2007. 450(7168): p. 402-406. Boriskina, S.V. and B.M. Reinhard, Spectrally and spatially configurable superlenses for optoplasmonic nanocircuits. Proc. Natl. Acad. Sci. USA, 2011. 108(8): p. 3147-3151.
Spasers:Stockman, M.I., Spasers explained. Nat Photon, 2008. 2(6): p. 327-329.Plasmonic particles on demand:Luther, J.M., et al., Localized surface plasmon resonances arising from free carriers in doped quantum dots. Nat Mater, 2011. 10(5): p. 361-366.
finally, Metamaterials is a huge area in itself – could be a separate class